Which of the following numbers is a factor of 190? ${3,4,7,10,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $190$ by each of our answer choices. $190 \div 3 = 63\text{ R }1$ $190 \div 4 = 47\text{ R }2$ $190 \div 7 = 27\text{ R }1$ $190 \div 10 = 19$ $190 \div 13 = 14\text{ R }8$ The only answer choice that divides into $190$ with no remainder is $10$ $ 19$ $10$ $190$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $190$ $190 = 2\times5\times19 10 = 2\times5$ Therefore the only factor of $190$ out of our choices is $10$. We can say that $190$ is divisible by $10$.